Examples
- because there is one partition of the set { 1, 2, 3 } that has a single block of size 3, there are three partitions of { 1, 2, 3 } that split it into a block of size 2 and a block of size 1, and there is one partition of { 1, 2, 3 } that splits it into three blocks of size 1.
- If bn = 2n(n−1)/2 is the number of graphs whose vertices are a given n-point set, then an is the number of connected graphs whose vertices are a given n-point set.
- There are numerous variations of the previous example where the graph has certain properties: for example, if bn counts graphs without cycles, then an counts trees (connected grphs without cycles).
- If bn counts directed graphs whose edges (rather than vertices) are a given n point set, then an counts connected directed graphs with this edge set.
Read more about this topic: Exponential Formula
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